Elliptic curve isogeny class with Cremona label 207368e (LMFDB label 207368.i)

• Label: 207368e
• Number of curves: $2$
• Conductor: $207368$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 207368e have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 207368e do not have complex multiplication.

Modular form 207368.2.a.e

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 207368e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
207368.i2	207368e1	\([0, 1, 0, -68232712, 216915221760]\)	\(1969910093092/7889\)	\(140694515703641424896\)	\([2]\)	\(12165120\)	\(3.0775\)	\(\Gamma_0(N)\)-optimal
207368.i1	207368e2	\([0, 1, 0, -69269552, 209981665312]\)	\(1030541881826/62236321\)	\(2219878068772054402009088\)	\([2]\)	\(24330240\)	\(3.4241\)